Domain Decomposition Preconditioning for Discontinuous Galerkin Approximations of Convection-Diffusion Problems

2009 ◽  
pp. 259-266 ◽  
Author(s):  
Paola F. Antonietti ◽  
Endre Süli
Keyword(s):  
Domain Decomposition ◽  
Discontinuous Galerkin ◽  
Convection Diffusion ◽  
Galerkin Approximations ◽  
Diffusion Problems

scholarly journals Ana posteriorierror bound for discontinuous Galerkin approximations of convection–diffusion problems

2017 ◽  
Vol 39 (1) ◽  
pp. 34-60
Author(s):  
Emmanuil H Georgoulis ◽  
Edward Hall ◽  
Charalambos Makridakis
Keyword(s):  
Discontinuous Galerkin ◽  
Convection Diffusion ◽  
Galerkin Approximations ◽  
Diffusion Problems

COMPARISON BETWEEN GLOBAL, CLASSICAL DOMAIN DECOMPOSITION AND LOCAL, SINGLE AND DOUBLE COLLOCATION METHODS BASED ON RBF INTERPOLATION FOR SOLVING CONVECTION-DIFFUSION EQUATION

2008 ◽  
Vol 19 (11) ◽  
pp. 1737-1751 ◽  
Author(s):  
GAIL GUTIERREZ ◽  
WHADY FLOREZ
Keyword(s):  
Diffusion Equation ◽  
Domain Decomposition ◽  
Mixed Boundary ◽  
Domain Decomposition Method ◽  
Collocation Methods ◽  
Special Treatment ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Full Domain ◽  
Diffusion Problems

This work presents a performance comparison of several meshless RBF formulations for convection-diffusion equation with moderate-to-high Peclet number regimes. For the solution of convection-diffusion problems, several comparisons between global (full-domain) meshless RBF methods and mesh-based methods have been presented in the literature. However, in depth studies between new local RBF collocation methods and full-domain symmetric RBF collocation methods are not reported yet. The RBF formulations included: global symmetric method, symmetric double boundary collocation method, additive Schwarz domain decomposition method (DDM) when it is incorporated into two anterior approaches, and local single and double collocation methods. It can be found that the accuracy of solutions deteriorates as Pe increases, if no special treatment is used. From the numerical tests, it seems that the local methods, especially the derived double collocation technique incorporating PDE operator, are more effective than full domain approaches even with iterative DDM in solving moderate-to-high Pe convection-diffusion problems subject to mixed boundary conditions.

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